You can not prove or disprove anything in existence or theory with out knowledge of everything and knowledge is infinite therefore a ever evolving theory is all we have. So to say something is impossible or untrue would conclude you know everything which no one does so keep a open mind, thats all humanity has left… A closed ignorant mind could mean the end…
While you cannot, in reality, prove a negative there is such a thing as weighing up rationality.
If I claimed to be Superman, would you believe me? And no, I refuse to fly, bend iron bars or outrun a speeding train in anyone's presence. But I am Superman.
Believe me? Doubtful. If I claimed the centre of the Earth was made of chocolate and inhabited with Umpalumpas, I doubt you'd believe that either.
We have a great deal of information about the centre of the Earth and even more the properties of the crust, particularly since satellites now allow for detailed measurements of things like gravitational and magnetic anomalies (often an indication of ore or oil deposits). None of them point towards the Earth being hollow and there being openings near the poles.
Then throw in the fact that there's no known natural mechanism to create such a thing. Why would the Earth be hollow? Why did it not collapse into a solid sphere when it was formed? What is making it stable? How come we measure earthquake propogation through the middle of it?
So while it's doubtful we'll ever tunnel down to find out, only people who put rationality and evidence aside will serious entertain such notions.
Who by the way has found a way to fund a expedition to the north pole via a Russian Nuclear Ice Breaker in search of many things including the "Opening". July 2008.
Is the expedition primarily for other things and he's just tagging along hoping to see something related to a hollow Earth? I very much doubt the Russian government would give use of a nuclear sub just to test the hollow Earth hypothesis. They might do things differently from us but they aren't wacko.